Question

Пусть x1 и x2- корни уравнения 3x²+8x-1=0. Не решая уравнения, найдите x1x2³ и x2x1³

Answer 1

Йоу ку

1) $\frac{1}{x_{1}}+\frac{1}{x_{2}} =\frac{x_{2}+x_{1}}{x_{1}x_{2}}=\frac{-\frac{b}{a}}{\frac{c}{a}} =\frac{-b}{c}=\frac{-8}{-1}=8$

2) $x_{1}x_{2}^3+x_{1}^3x_{2}=x_{1}x_{2}(x_{1}^2+x_{2}^2)=x_{1}x_{2}[(x_{1}+x_{2})^2-2x_{1}x_{2}]=\frac{c}{a}*[(-\frac{b}{a})^2-2\frac{c}{a}]=\frac{c*(b^2-2c)}{a^2}=\frac{b^2c-2c^2}{a^2}=\frac{8^2*(-1)-2*(-1)^2}{3^2}=\frac{-64-2}{9}=\frac{22}{3}$